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# Topic: Z notation

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 NationMaster - Encyclopedia: Set builder notation In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by indicating the properties that its members must satisfy. The simplest sort of set-builder notation is {x : P(x)}, where P is a predicate in one variable. The notation can be complicated, especially as in the previous example, and abbreviations are often employed when context indicates the nature of a variable. www.nationmaster.com /encyclopedia/Set_builder-notation   (0 words)

 Notation Software -- Company Information Notation Software is a privately held company founded in 1994 by Mark Walsen, a software professional with a passion for music. The focus at Notation Software is the promotion of the computer as an active musical companion for the everyday musician who reads music. Notation Software will continue to lead the way with music software products created for the everyday musician – designed to allow all of us to use computers to enjoy music more. www.notation.com /Company.htm   (0 words)

 What is Z? What is Z? What is Z? Z (pronounced zed) is a set of conventions for presenting mathematical text, chosen to make it convenient to use simple mathematics to describe computing systems. Z is just a notation, it is not a method; the Z notation can support many different methods. The first Z reference manual to be widely published benefited from this long experience when it finally appeared in 1989. staff.washington.edu /~jon/z-book/what-is-z.html   (641 words)

 Kids.Net.Au - Encyclopedia > Z notation The Z notation (pronounced 'zed', not 'zee', even in the United States) is a formal specification language used for describing and modelling computing systems. All expressions in Z notation are typed, thereby avoiding some paradoxes of naive set theory. Although Z notation uses many non-ASCII symbols, the specification includes suggestions for rendering the Z notation symbols in ASCII and in LaTeX. www.kids.net.au /encyclopedia-wiki/z_/Z_notation   (196 words)

 z notation sample - z notation function The Z notation z notation partial function full function difference (universally pronounced zed, z notation sample named after Zermelo-Fränkel set theory) is a formal specification language used for describing and modelling computing systems. Z was developed by the Programming Research Group at Oxford University in the late 1970s and is based on the standard mathematical notation used in axiomatic set theory, lambda calculus, and first-order predicate logic. Z contains a standardized catalog (called the mathematical toolkit) of commonly used mathematical functions and predicates. www.infotechloco.com /Inf-Programming-U---Z/Z-notation.html   (187 words)

 Abbreviating Z When students are asked to write their first Z specification, they often produce formulae that are not Z. Some of these formulae have no obvious meaning; others make sense, but happen not to conform to Z syntax and semantics. Students naturally borrow concepts and notations from SML, which is a declarative language, and attempt to use them in Z. Unfortunately, the correct Z equivalent can be verbose and clumsy in comparison, particularly when defining a function. The standard Z form can be used where type inference would fail, or else where it is desired to emphasise the types involved. www.ecs.soton.ac.uk /publications/rj/1994/decsys/gravell/gravell.html   (0 words)

 FREENIX Track: USENIX 2002 Annual Technical Conference - Paper Thus, using the Z notation to construct a lightweight problem model can enable the construction of an algorithm for controlling client thread access to the server that has a high likelihood of correctness in a situation where user testing is likely to be ineffective. For Z novices, it may be desirable to consult one of the Z references cited in Section 2 before attempting to read this section. Z is nice for modeling the XCB pseudo-code, because states are modeled as changing instantaneously: this avoids any explicit mention of mutual exclusion via mutexes at the model level. www.usenix.org /events/usenix02/tech/freenix/full_papers/massey/massey_html/index.html   (6197 words)

 [No title] I recommend the first chapter of the Z reference manual, zrm.pdf, as an excellent tutorial on Z.) Interestingly, the Z standard uses a version of the same Z notation (supplemented with the syntactic categories of Z as types) as the metalanguage for defining Z itself. Although that metalanguage is not presented as a standardized language in the Z document, a similar approach could be formalized as part of the more ambitious goals we have envisioned for the full Common Logic standard. Furthermore, Appendix A of the ISO Z standard is devoted to the LaTeX mark-up for formatting and printing Z notation. grimpeur.tamu.edu /pipermail/kif/2003-January.txt   (1798 words)

 The Dispatch - Serving the Lexington, NC - News   (Site not responding. Last check: ) The Z notation (universally pronounced zed, named after Zermelo-FrÃ¤nkel set theory) is a formal specification language used for describing and modelling computing systems. Z was originally proposed by Jean-Raymond Abrial in 1977 with the help of Steve Schuman and Bertrand Meyer A valuable resource for newcomers interested in learning Z is The Z Notation: a reference manual. www.the-dispatch.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Z_notation   (290 words)

 Formatting Math as Text: Set and Logical Notation While these topics do not properly belong within the subject of algebra, their notation often arises in algebra courses. When you are writing an open interval, use parentheses, and note that "this is an interval", to differentiate an interval from a point. If you use "Q" for "the set of all rational numbers" (that is, the set of all fractions), define the notation. www.purplemath.com /modules/mathtext2.htm   (0 words)

 CADiZ: ISO Standard Z   (Site not responding. Last check: ) ZRM notation is used largely for producing abstract specifications of systems, where the emphasis is on the use of schemas and constraints on them rather than particular bindings, those being more specific and concrete. However, Z can be used in other ways and in other contexts, for example, the author has used it in reasoning about a relational database, where the rows of a table were modelled by the bindings of a schema. In ISO Standard Z, one of these schemas used as a predicate is equivalent to the corresponding predicate involving the operand schemas used as predicates. www-users.cs.york.ac.uk /~ian/cadiz/standard.html   (4421 words)

 International standard date and time notation The time notation described here is already the de-facto standard in almost all countries and the date notation is becoming increasingly popular. In some applications, a date notation is preferred that uses only the year and the day of the year between 001 and 365 (366 in leap years). Note: The Z stands for the “zero meridian”, which goes through Greenwich in London, and it is also commonly used in radio communication where it is pronounced “Zulu” (the word for Z in the international radio alphabet). www.cl.cam.ac.uk /~mgk25/iso-time.html   (0 words)

 1.2 Notation The descriptions of lexical analysis and syntax use a modified BNF grammar notation. ) is used to separate alternatives; it is the least binding operator in this notation. Even though the notation used is almost the same, there is a big difference between the meaning of lexical and syntactic definitions: a lexical definition operates on the individual characters of the input source, while a syntax definition operates on the stream of tokens generated by the lexical analysis. www.python.org /doc/2.4.3/ref/notation.html   (0 words)

 comp.specification.z Frequently Asked Questions (FAQ) Z (pronounced `zed') is a formal specification notation based on set theory and first order predicate logic. Various tools for formatting, type-checking and aiding proofs in Z are available under: http://vl.zuser.org/#tools This includes links to a number of LaTeX style files which support the Z notation. Some people have looked at animating subsets of Z for rapid prototyping purposes, using logic and functional programming for example, but this is not really the major point of Z, which is to increase human understandability of the specified system and allow the possibility of formal reasoning and development. www.faqs.org /faqs/z-faq   (0 words)

 The World Wide Web Virtual Library: The Z notation Z is a formal (i.e., mathematical) specification notation used by industry (especially in high-integraity systems) as part of the software (and hardware) development process in both Europe and the US. A shallow embedding of Z in the higher-order logic theorem prover Isabelle. ZTC is a Z type-checker available free of charge for educational and non-profit uses. www.afm.sbu.ac.uk /z   (0 words)

 The World Wide Web Virtual Library: The Z notation Z is now used by industry as part of the software (and hardware) development process in both Europe and the US. The use of Z has resulted in a UK Queen's Award for Technological Achievement in 1992 for its use in the IBM CICS project and contributed towards one in 1990 for its use to specify the IEEE Standard for Binary Floating-Point Arithmetic (see Technical Monograph PRG-58). A shallow embedding of Z in the higher-order logic theorem prover Isabelle. www.comlab.ox.ac.uk /archive/z.html   (2071 words)

 Web Services Description Language (WSDL) Version 2.0 Part 1: Core Language Z Notation is a formal specification language that is based on standard mathematical notation. The Z Notation was used to improve the quality of the normative text that defines the Component Model, and to help ensure that the test suite covered all important rules implied by the Component Model. A Z generic definition defines an object whose type depends on the types of one or more sets that are given as arguments to the definition. www.w3.org /TR/2006/CR-wsdl20-20060106/wsdl20-z.html   (4756 words)

 Z notation - Definition, explanation The Z notation (universally pronounced zed) is a formal specification language used for describing and modelling computing systems. Z was developed by the Programming Research Group at Oxford University in the late 1970s and is based on the standard mathematical notation used in axiomatic set theory, lambda calculus, and first-order predicate logic. The formal specification notation Z is based on Zermelo-Fraenkel set theory and... www.calsky.com /lexikon/en/txt/z/z_/z_notation.php   (560 words)

 Understanding Z - Cambridge University Press The Z notation, a language for expressing mathematical specifications of computing systems, is gaining widespread popularity in both industry and the academic world. By providing a formal semantics for Z, this book justifies the claim that Z is a precise specification language, and provides a standard framework for understanding Z specifications. Z is compared with other methods such as VDM and CLEAR, and in the final chapter, a number of studies in Z style are presented to show that Z can be used in a wide variety of specification tasks. www.cambridge.org /catalogue/catalogue.asp?isbn=0521334292   (161 words)

 Introduction to DSP - IIR filters: The z transform   (Site not responding. Last check: ) The complex variable z is shown as a vector on the Argand diagram. So the z transform of the last signal value can be obtained by multiplying the z transform of the current value by (1/z). This is why, in the filter diagram, the delay elements are represented formally using the 1/z notation. www.bores.com /courses/intro/iir/5_ztran.htm   (144 words)

 Notation for the Mixed Model This section introduces the mathematical notation used throughout this chapter to describe the mixed linear model. The model matrix Z is set up in the same fashion as X, the model matrix for the fixed-effects parameters. By appropriately defining the model matrices X and Z, as well as the covariance structure matrices G and R, you can perform numerous mixed model analyses. www.okstate.edu /sas/v7/sashtml/books/stat/chap37/sect3.htm   (309 words)

 Special Symbols The notation "OR " is used to denote one of several possible alternate results. The use of this notation is intended to disguise small differences in interactive input and output behavior between implementations. How that newline character is interactively entered is an implementation-defined detail of the user interface, but in that case, either the notation "" or "[Return]" might be used. www.franz.com /support/documentation/6.2/ansicl/subsubse/specials.htm   (466 words)

 RUCS: Z notation   (Site not responding. Last check: ) TrueType Z fonts are available on-line for PC Windows and Macs if you wish to do your assessment using MS Word or other similar word processors. The assessment is a practical to develop, type-check and partially animate a Z specification. The LaTeX source for a initial version of a Z specification (based on Exercise 4) is available to start you off. www.jpbowen.com /teaching/z.html   (753 words)

 Notation Software, Inc. -- Music software for musicians Easily and fully edit both the notation and playback sound (MIDI) of music scores. Also enjoy all of the features of Notation Musician (see below). Print the music for yourself, and print parts for members of your vocal or instrumental group. www.notation.com   (151 words)

 Notation of DATE What follows is a query, and a suggestion, about the 'notation of date'. For my benefit, can anyone clarify the ORIGIN of the 'notation of date' used in the USA that is: MMM DD, YY e.g. In my Navy days at sea, the notation for time zone was: Letter (hours) Example: K(-10) meaning zone Lima (subtract 10 to get Z or GMT or UTC) K is our normal/current time in eastern Australia. www.amsat.org /amsat/archive/amsat-bb/200206/msg00409.html   (0 words)

 Inequalities. Set Notation etc. To indicate that an endpoint is included, we use a square bracket; to exclude an endpoint, we use parentheses. Z denotes the integers 0, 1, -1, 2, -2,.... Beyond that, set notation uses descriptions: the interval (-3,5] is written in set notation as www.sosmath.com /algebra/inequalities/ineq02/ineq02.html   (0 words)

 Imagine the Universe! Dictionary The notation separates a number into two parts: a decimal fraction, usually between 1 and 10, and a power of ten. The radiated power P (rate of emission of electromagnetic energy) of a hot body is proportional to the radiating surface area, A, and the fourth power of the thermodynamic temperature, T. The constant of proportionality is the Stefan-Boltzmann constant. z = (delta-lambda)/lamda = (sqrt(1+v/c) / sqrt(1-v/c)) - 1. imagine.gsfc.nasa.gov /docs/dict_qz.html   (3025 words)

 Begriffsschrift   (Site not responding. Last check: ) Begriffsschrift is the title of a short book on logic by Gottlob Frege, published in 1879, and is also the name of the formal system set out in that book. Begriffsschrift is usually translated as concept writing or concept notation; the full title of the book identifies it as "a formula language, modelled on that of arithmetic, of pure thought." The Begriffsschrift was arguably the most important publication in logic since Aristotle founded the subject. Although Frege does not make these applications here, it is clear that these results are intended to be applied in his later work on the foundations of arithmetic. www.dejavu.org /cgi-bin/get.cgi?ver=93&url=http%3A%2F%2Farticles.gourt.com%2Fen%2FBegriffsschrift   (992 words)

 WG 19 Home Page Z was used in the 1980s in a number of industrial projects to assist developers of hardware and software systems. The notation was defined formally by Spivey in his book Understanding Z (1988), and this was followed by an informal description and guide to the notation in The Z Notation: A Reference Manual (1989, 2nd edn 1992). Industrial users of Z pressed the PRG, guardians of the notation, to produce a definitive statement about the content of the Z language, and this resulted in a collaboration of academic and industrial users in the ZIP project. anubis.dkuug.dk /JTC1/SC22/WG19   (571 words)

 Open Directory - Computers: Programming: Languages: Z   (Site not responding. Last check: ) Standard for Z Notation - International Z Notation standardization effort finished in 2002 and yielded The ISO/IEC Z Standard. Z Family on the Web with Their UML Photos - Treats building lightweight tools such as Web browser systems for formal specifications and methods. The Z Notation - The formal specification notation Z is based on Zermelo-Fraenkel set theory and first order predicate logic. dmoz.org /Computers/Programming/Languages/Z   (469 words)

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